A Local Tire Dealer Wants to Predict the Number of Tires

question 72

Short Answer

A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results.
∑X = 24
∑X² = 124
∑Y = 42
∑Y² = 338
∑XY = 196
Calculate the coefficient of determination.

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Definitions:

Economic Profit

The difference between total revenue and total costs, including both explicit and implicit costs, representing the financial gain exceeding the opportunity costs of resources.

MR = MC

An economic principle stating that the maximum profit occurs where marginal revenue equals marginal cost, guiding firms on the optimal level of output.

Output

The total amount of goods or services produced by a firm, industry, or economy within a given period.

Short-Run Supply

The supply of goods that varies with changes in price in the short term, where at least one factor of production is fixed.